Abstract

We propose a multi-photon interferometer with a generalized C-SWAP operation that can estimate Tr[ρ1ρ2ρn], a nonlinear functional of n photonic density matrices. The scheme is demonstrated for three single-photon states whose overlap is experimentally measured as the interference visibility of a control qubit encoded into photonic paths. The validity of this method is verified by comparing the visibility with the results of Hong-Ou-Mandel experiments.

© 2013 OSA

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  1. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76, 4656–4659 (1996).
    [CrossRef] [PubMed]
  2. J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett.64, 2495–2498 (1990).
    [CrossRef] [PubMed]
  3. I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
    [CrossRef] [PubMed]
  4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
    [CrossRef] [PubMed]
  5. P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).
  6. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  7. M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
    [CrossRef]
  8. S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
    [CrossRef] [PubMed]
  9. K. N. Cassemiro, K. Laiho, and C. Silberhorn, “Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference,” New J. Phys.12, 113052 (2010).
    [CrossRef]
  10. A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
    [CrossRef] [PubMed]
  11. R. Filip, “Overlap and entanglement-witness measurements,” Phys. Rev. A65, 062320 (2002).
    [CrossRef]
  12. Y.-X. Gong, G.-C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A78, 012305 (2008).
    [CrossRef]
  13. J. Fiurášek, “Linear optical fredkin gate based on partial-SWAP gate,” Phys. Rev. A78, 032317 (2008).
    [CrossRef]
  14. X.-Q. Shao, L. Chen, S. Zhang, and Y.-F. Zhao, “Swap gate and controlled swap gate based on a single resonant interaction with cavity quantum electrodynamics,” Physica Scripta79, 065004 (2009).
    [CrossRef]
  15. B. Wang and L.-M. Duan, “Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation,” Phys. Rev. A75, 050304 (2007).
    [CrossRef]
  16. F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
    [CrossRef]
  17. S. M. Lee, H. S. Park, J. Cho, Y. Kang, J. Y. Lee, H. Kim, D.-H. Lee, and S.-K. Choi, “Experimental realization of a four-photon seven-qubit graph state for one-way quantum computation,” Opt. Express20, 6915–6926 (2012).
    [CrossRef] [PubMed]
  18. Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A60, 593–604 (1999).
    [CrossRef]
  19. C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
    [CrossRef]
  20. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
    [CrossRef] [PubMed]

2013 (1)

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

2012 (1)

2011 (1)

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

2010 (1)

K. N. Cassemiro, K. Laiho, and C. Silberhorn, “Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference,” New J. Phys.12, 113052 (2010).
[CrossRef]

2009 (1)

X.-Q. Shao, L. Chen, S. Zhang, and Y.-F. Zhao, “Swap gate and controlled swap gate based on a single resonant interaction with cavity quantum electrodynamics,” Physica Scripta79, 065004 (2009).
[CrossRef]

2008 (3)

Y.-X. Gong, G.-C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A78, 012305 (2008).
[CrossRef]

J. Fiurášek, “Linear optical fredkin gate based on partial-SWAP gate,” Phys. Rev. A78, 032317 (2008).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

2007 (1)

B. Wang and L.-M. Duan, “Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation,” Phys. Rev. A75, 050304 (2007).
[CrossRef]

2004 (1)

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

2003 (2)

F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
[CrossRef]

M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
[CrossRef]

2002 (2)

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

R. Filip, “Overlap and entanglement-witness measurements,” Phys. Rev. A65, 062320 (2002).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

1999 (1)

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A60, 593–604 (1999).
[CrossRef]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76, 4656–4659 (1996).
[CrossRef] [PubMed]

1990 (1)

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett.64, 2495–2498 (1990).
[CrossRef] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Alves, C. M.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Aparo, L.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Borjemscaia, N.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Cassemiro, K. N.

K. N. Cassemiro, K. Laiho, and C. Silberhorn, “Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference,” New J. Phys.12, 113052 (2010).
[CrossRef]

Caves, C. M.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

Chen, L.

X.-Q. Shao, L. Chen, S. Zhang, and Y.-F. Zhao, “Swap gate and controlled swap gate based on a single resonant interaction with cavity quantum electrodynamics,” Physica Scripta79, 065004 (2009).
[CrossRef]

Cho, J.

Choi, S.-K.

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

de Riedmatten, H.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

Deuar, P.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

Du, J.-F.

F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
[CrossRef]

Duan, L.-M.

B. Wang and L.-M. Duan, “Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation,” Phys. Rev. A75, 050304 (2007).
[CrossRef]

Dušek, M.

M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
[CrossRef]

Ekert, A. K.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Filip, R.

M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
[CrossRef]

R. Filip, “Overlap and entanglement-witness measurements,” Phys. Rev. A65, 062320 (2002).
[CrossRef]

Fiurášek, J.

J. Fiurášek, “Linear optical fredkin gate based on partial-SWAP gate,” Phys. Rev. A78, 032317 (2008).
[CrossRef]

M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
[CrossRef]

Flagg, E. B.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Gisin, N.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

Gong, Y.-X.

Y.-X. Gong, G.-C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A78, 012305 (2008).
[CrossRef]

Guo, G.-C.

Y.-X. Gong, G.-C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A78, 012305 (2008).
[CrossRef]

Han, R.-D.

F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
[CrossRef]

Hendrych, M.

M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, “Simple optical measurement of the overlap and fidelity of quantum states,” Phys. Lett. A310, 95–100 (2003).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Horodecki, M.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Horodecki, P.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Kang, Y.

Kim, H.

Kwek, L. C.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Kwiat, P. G.

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76, 4656–4659 (1996).
[CrossRef] [PubMed]

Laiho, K.

K. N. Cassemiro, K. Laiho, and C. Silberhorn, “Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference,” New J. Phys.12, 113052 (2010).
[CrossRef]

Lee, D.-H.

Lee, J. Y.

Lee, S. M.

Legré, M.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

Ling, A.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Marcikic, I.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

Marrucci, L.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Mattle, K.

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76, 4656–4659 (1996).
[CrossRef] [PubMed]

Migdall, A.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Milburn, G. J.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

Muller, A.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Munro, W.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

Nemoto, K.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Oi, D. K. L.

A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, “Direct estimations of linear and nonlinear functionals of a quantum state,” Phys. Rev. Lett.88, 217901 (2002).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A60, 593–604 (1999).
[CrossRef]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Park, H. S.

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Polyakov, S. V.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Ralph, T. C.

Y.-X. Gong, G.-C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A78, 012305 (2008).
[CrossRef]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett.64, 2495–2498 (1990).
[CrossRef] [PubMed]

Rhee, J.-K.

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A60, 593–604 (1999).
[CrossRef]

Rungta, P.

P. Rungta, W. Munro, K. Nemoto, P. Deuar, G. J. Milburn, and C. M. Caves, Qudit Entanglement (Springer Berlin Heidelberg, 2001).

Santamato, E.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Sciarrino, F.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Shao, X.-Q.

X.-Q. Shao, L. Chen, S. Zhang, and Y.-F. Zhao, “Swap gate and controlled swap gate based on a single resonant interaction with cavity quantum electrodynamics,” Physica Scripta79, 065004 (2009).
[CrossRef]

Silberhorn, C.

K. N. Cassemiro, K. Laiho, and C. Silberhorn, “Accessing the purity of a single photon by the width of the Hong-Ou-Mandel interference,” New J. Phys.12, 113052 (2010).
[CrossRef]

Solomon, G. S.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Spagnolo, N.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Tapster, P. R.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett.64, 2495–2498 (1990).
[CrossRef] [PubMed]

Tittel, W.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett.93, 180502 (2004).
[CrossRef] [PubMed]

Van Keuren, E.

S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, “Coalescence of single photons emitted by disparate single-photon sources: The example of InAs quantum dots and parametric down-conversion sources,” Phys. Rev. Lett.107, 157402 (2011).
[CrossRef] [PubMed]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

Vitelli, C.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nature Photon.7, 521–526 (2013).
[CrossRef]

Wang, B.

B. Wang and L.-M. Duan, “Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation,” Phys. Rev. A75, 050304 (2007).
[CrossRef]

Wang, L. J.

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A60, 593–604 (1999).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001).
[CrossRef] [PubMed]

Weinfurter, H.

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76, 4656–4659 (1996).
[CrossRef] [PubMed]

Wu, J.-H.

F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
[CrossRef]

Xue, F.

F. Xue, J.-F. Du, X.-Y. Zhou, R.-D. Han, and J.-H. Wu, “Experimentally obtaining the likeness of two unknown qubits on a nuclear-magnetic-resonance quantum information processor,” Chinese Phys. Lett.20, 1669–1671 (2003).
[CrossRef]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Zbinden, H.

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Zhao, Y.-F.

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Nature (1)

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Nature Photon. (1)

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Figures (6)

Fig. 1
Fig. 1

Interferometers for overlap estimation of (a) two photons and (b) n photons. NPBS: non-polarizing beam splitter, PS: phase shifter, D: single photon counter, CC: coincidence counter.

Fig. 2
Fig. 2

Experimental setup. The components in the dashed box are used only during the alignment procedures. BBO: β-BaB2O4, IF: interference filter, ODi: variable optical delay, HWP: half-wave plate, Ii: input port, NPBS: non-polarizing beam splitter, PS: phase shifter, Oi: output port, SMF: single-mode fiber, FBS: fiber beam splitter, Di: single photon counter, CC: coincidence counter.

Fig. 3
Fig. 3

Measured interference fringes. The polarizations of photons 1 and 3 are fixed to be horizontal. The polarization of photon 2 is varied: (a) 0°, (b) 30°, (c) 60°, and (d) 90°.

Fig. 4
Fig. 4

Interference fringes with the polarizations of all input photons linear along 45° with respect to the horizontal axis.

Fig. 5
Fig. 5

Interference fringes with varying the temporal/spectral overlap between photons. Photon 3 is temporally delayed by (a) + 26 μm and (b) − 26 μm. (c) The half-maximum filter bandwidth of the interference filters for photons 3 and 4 is changed from 5 nm to 10 nm.

Fig. 6
Fig. 6

Hong-Ou-Mandel interferences by two photons from (a) a single pair (photons 1 and 2) and (b) different pairs (photons 2 and 3): Coincidence counts in (a) and (b) are measured by the two photon counters connected to O1 and O2, respectively, as shown in Fig. 2.

Equations (6)

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| Ψ f 2 = 1 4 ( e i ϕ | ψ 1 D 1 | ψ 2 D 2 + | ψ 2 D 1 | ψ 1 D 2 ) .
P f ( 2 ) = { 1 8 ( 1 + | ψ 1 | ψ 2 | 2 cos ϕ ) for pure states , 1 8 ( 1 + Tr [ ρ 1 ρ 2 ] cos ϕ ) for mixed states ,
| Ψ f ( n ) = 1 2 n ( e i ϕ | ψ 1 D 1 | ψ n D n + | ψ 2 D 1 | ψ n D n 1 | ψ 1 D n ) .
P f ( n ) = { 2 ( 2 n 1 ) ( 1 + ψ 1 | ψ 2 ψ 2 | ψ 3 ψ n | ψ 1 cos ϕ ) for pure states , 2 ( 2 n 1 ) ( 1 + Tr [ ρ 1 ρ 2 ρ n ] cos ϕ ) for mixed states .
Tr [ ρ 1 ρ 2 ρ n ] = Tr [ | ψ 1 ψ 1 | | ψ 2 ψ 2 | | ψ n ψ n | ] = ψ 1 | ψ 2 ψ 2 | ψ 3 ψ n | ψ 1 .
Tr [ ρ 1 ρ 2 ρ n ] Tr [ ρ 1 ρ 2 ] Tr [ ρ 2 ρ 3 ] Tr [ ρ n ρ 1 ] .

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